Method and a system for a receiver design in bandwidth constrained communication systems

ABSTRACT

The present invention relates to a method of improving the performance in bandwidth constrained communication systems while reducing the complexity of the equalizer used for information retrieval, as well as to improving the capacity of communication systems. The said properties are achieved by appropriate information encoding, prior to signal shaping before transmission, whereas the equalizer complexity is reduced by applying the intersymbol interference shortening filter prior to the information retrieving equalization. A proper combination of the recounted elements is capable of providing a qualitatively improved and previously unsuspected performance, as compared to its constituent elements.

CROSS-REFERENCE TO RELATED APPLICATIONS

The present application claims the benefit of U.S. ProvisionalApplication Ser. No. 61/780,918 by Nikola Alic and John G. Proakis,filed on Mar. 13, 2013, and entitled “A Method and a System for aReceiver Design in Bandwidth Constrained Communication Systems,” thecontents of which are incorporated herein in their entirety by thisreference.

FIELD OF THE INVENTION

The invention relates generally to communication systems and moreparticularly to detection in bandwidth constrained communicationsystems. The invention is specifically aimed at availing both animproved performance in spectrally efficient bandwidth constrainedcommunication systems, as well as at simplifying the receiver structurein these systems. The method is of particular interest for bandwidthconstrained or narrowly filtered communication systems.

BACKGROUND OF THE INVENTION

Bandwidth constrained or narrowly filtered communication systems aredefined in U.S. Pat. No. 8,155,530 to Alic et al., incorporated hereinby this reference.

Ability to reliably transmit a high quantity of information over a givenbandwidth is the single most important aim of communication systems. Indesigning the communication systems, predominantly modulation formatswithout memory are used. As is well known, these systems, often based onquadrature amplitude modulation (QAM) cannot reach theoretical bounds ofspectral efficiency. On the other hand, when mated with verysophisticated encoding schemes that jointly optimize the modulation anderror control coding (ECC), communication systems without memory areknown to perform closer to the theoretical bounds. The error-controlcodes append redundant information bits, or symbols, so as to achieveresilience and/or an improved performance in the presence of hindrancesin the process of the information transfer, such as noise anddistortions. Specifically, it has recently been demonstrated thatutilization of more than one error control code, in the encodingprocess, in a construction best described as multiple level informationprotection, can yield an improved performance, especially if mated withthe so called iterative decoding, in which the reliability estimates onthe received information symbols are exchanged between the constituentcodes' decoders multiple times, with an improved estimate on theinformation symbols being obtained with each additional iteration. Inparticular, in the context of iterative decoding, it is often said,owing to the particular encoding implementation that the constituentcodes are concatenated. In particular, the process of concatenation isachieved by constructs called interleavers that in effect permute theorder of either the input information symbol prior to encoding, orpermute the order of encoded information symbols. Conversely, the actionof restoring the input information order is achieved by de-interleaversat the receiving end. The process of iterative decoding encompasses theinterleaving and the de-interleaving process in that passing of thecodewords between multiple constituent decoders is assumed to includethe permutation of the relevant information symbols so as to becorresponding to the pertinent constituent codes.

The key aspect of the present invention is that if bandwidthconstriction (or introducing memory into the communication system bydesign) is used appropriately in conjunction with error control coding—anovel, previously unsuspected quality is attained in that the describedsimple arrangement can operate even closer to the theoretical boundsthan the systems mentioned above. Thus, the main characteristic of thepresent invention is its ability to provide outstanding performance andcapacity, based on a simpler design than existing communication systems'concepts. On the other hand, bandwidth constrained communication systemsrely on equalization to mitigate the effect of bandwidth limitation. Inparticular, the systems with high spectral efficiency, or equivalently—aconsiderable amount of bandwidth limitation, can be affected bysignificant extension of the channel response duration, thus requiringlong, and/or complex equalization structures to appropriately handle theeffects of the induced intersymbol interference. Complex equalizers notonly contribute to a significant complexity increase and difficultpractical realization, but also increase the overall system powerconsumption. Consequently, the existing solutions fail to meet theindustry needs since, for high spectral efficiencies, they result inboth an inferior performance, as well as in overly intricate, and thushighly power hungry solutions.

Currently there are a number of solutions for improving capacity (i.e.the amount of information reliably transmittable over a givenbandwidth). Some of these solutions attempt to utilize modulationformats without memory, such as QAM, mentioned above, but thesesolutions fail to meet the needs of the industry because QAMs cannotoperate close enough to the theoretical bounds. Other solutions attemptto use specific (i.e. redundant) encoding for information in order toimprove performance, but these solutions are similarly unable to meetthe needs of the industry because they still cannot provide adequateperformance. Still other solutions seek to jointly optimize modulationand error control coding (ECC) by means of e.g., trellis codedmodulation, but these solutions also fail to meet some specific industryneeds because of the associated complexity of that solution.

The narrowly filtered, or bandwidth constrained systems with highspectral efficiency necessarily need to rely on equalization forinformation retrieval from severely distorted information-bearingwaveforms at the receiving end of the link. In addition there exist anumber of solutions for equalization in digital communication systemsaffected by intersymbol interference. Some of these solutions attempt tomitigate the effects of intersymbol interference by equalization thatcorresponds to the full extent of the channel response duration (interms of the number of symbol slots affected by intersymbolinterference), but these solutions fail to meet the needs of theindustry because a direct equalization often yields complex equalizationstructures. Other solutions attempt to use simpler equalizationstructures, but these solutions are similarly unable to meet the needsof the industry because they do not provide satisfactory performance.

The overall performance and the underlying complexity of the equalizerused in communication systems represent critical concerns in theirpractical realization, and are of particular importance for high speedsystems. The said properties translate to both higher reliability and/orcapacity in communication systems, as well as a lower receiver andsystem overall power dissipation and an easier practical implementation.Consequently, there currently exists a clear need in the industry formeans of improving the performance and capacity of communicationsystems, in addition to reducing the complexity of the underlyingdigital receivers.

In that respect, it would be desirable to have a composition that canhave a simpler design than the existing ones which/that can be used toprovide performance close to the theoretical bounds. Still further, itwould be desirable to have a compound that can be used as an add-onsolution to the existing systems and provide them with a superiorperformance.

In that respect, it would be desirable to have a composition that availsan improved performance and/or capacity which has a limited complexity.It would be desirable to have a composition that can have a simplerdesign than the existing ones which/that can be used to provideperformance close to the theoretical bounds. Furthermore, it would alsobe desirable to have a composition whose practical implementation isstraightforward. Still further, it would be desirable to have a compoundthat can be used as an add-on solution to the existing systems andprovide them with a superior performance. Furthermore, it would bedesirable to have a compound that introduces a low latency inprocessing. In summary, there currently exists a need in the industryfor a composition that is instrumental in providing an improvedperformance while forgoing a complex equalization structure and is, yet,capable of handling large amounts of intersymbol interference withlimited penalties.

SUMMARY OF THE INVENTION

The present invention advantageously fills the aforementioneddeficiencies by uniquely providing a superior system performance, withlower complexity, latency and power dissipation, and includes a specificreceiver design comprising an equalizer, an optional pre-processingapproach applied to the incoming waveforms, or samples, which availsutilization of a lower complexity information retrieving equalizer, aswell as the error control coder and decoder matched to the bandwidthconstrained channel. The present invention is a method for the receiverdesign in bandwidth restricted communication systems which by anappropriate combination of equalization and error control codingqualitatively improves the overall system performance and capacity. Thepresent invention also employs a digital reshaping at the receiver in aspecific way, so as to avail utilization of lower complexity informationretrieving equalizers in the receiver processing chain. The invention,broadly, consists of the following steps: (1) shortening of the channelresponse by means of a specific signal processing step; (2)equalization, or information retrieval by an appropriate equalizer and(3) error control decoding. Specifically in the case of time-varyingchannels, an update of the channel response shortening actionaccomplishing the target response, as well as the information retrievingequalizer, to the best of ability, or according to an optimization of acertain criterion might have to be performed periodically.

The present invention is unique in that it is different from other knownprocesses or solutions. More specifically, the present invention owesits uniqueness to the fact that it: (1) encompasses a particularcombination of processing steps (i.e. error control coding in bandwidthconstricted systems, intersymbol interference shortening andtrellis-based equalization) that provides a qualitatively novel andimproved, previously unsuspected, system performance; (2) enables asignificant complexity reduction of the information retrieving equalizerby introducing a pre-processing step of signal reshaping.

Among other things, it is an object of the present invention to improvethe overall system performance in highly spectrally efficient bandwidthrestricted communication systems.

It is further an objective of the present invention to adjust thereceived waveforms in bandwidth constrained communication systems byadaptive digital processing in a way that shortens the channel responseduration in terms of the number of symbol slots that at the same timedoes not suffer from any of the problems or deficiencies associated withprior solutions.

It is still further an object of the present invention to significantlysimplify the information retrieving equalization which is performedlater in the receiver processing chain (as shown in FIG. 1, below).

Further still, it is an object of the present invention to reduce thepower dissipation of the receiver.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention now will be described more fully hereinafter withreference to the accompanying drawings, which are intended to be read inconjunction with both this summary, the detailed description and anypreferred and/or particular embodiments specifically discussed orotherwise disclosed. This invention may, however, be embodied in manydifferent forms and should not be construed as limited to theembodiments set forth herein; rather, these embodiments are provided byway of illustration only and so that this disclosure will be thorough,complete and will fully convey the full scope of the invention to thoseskilled in the art.

FIG. 1 illustrates a general schematic of a digital communicationsystem.

FIG. 2 shows an example flow chart of channel response reshaping.

FIG. 3 shows an example of an outcome of channel response reshaping.

FIG. 4 illustrates an improved performance of the bandwidth constrainedsystem in the embodiment described in this invention (in solid lines),compared to performance of standard QAM systems (dashed lines), for sameinstances of spectral efficiencies.

DETAILED DESCRIPTION OF THE INVENTION

The present invention is directed at improving the performance ofbandwidth constrained systems and/or capacity of communication systemsin general.

In the preferred embodiment of the invention, the information is encodedby error-control redundant symbols having what is known as concatenated‘turbo’ structure (see FIG. 1), prior to the waveform shaping. Theshaping of the waveforms to be transmitted intentionally introducesmemory into the transmitted signals. At the receiving end, after severalstandard processing steps, the encoded information corrupted aftertransmission through the channel is estimated by an informationretrieving block that is implemented as a maximum a posteriori (i.e.BCJR) equalizer and is passed to the decoding block which iterativelyimproves the estimates of the received data, whereas the estimates canfurther be improved by including the information retrieving equalizerinto the iterative detection. As a final outcome, after a sufficientnumber of iterations, the highly reliable information symbols emanatingfrom the iterative decoding and detection process are output as thereceived information/data.

It ought to be emphasized that both of the key components of the presentinventions have been known in the past (i.e. bandwidth constriction anderror control coding). What makes the present invention unique is anovel scientific finding that a particular combination of the notedcomponents can produce previously unsuspected and certainly never beforedemonstrated performance. In that respect, the present invention isbased on a novel rigorously obtained theoretical result marking a sharpdifference to the previous similar and dissimilar systemimplementations.

In an alternative embodiment an additional processing step can beadopted prior to the information retrieving equalizer. The purpose ofthe additional processing step is to shorten the channel response, and,thus avail utilization of a less complex information-retrievingequalizer. The response shortening processor is in a preferredembodiment realized as a finite impulse response filter, however othersimilar approaches achieving the same effect and for the same purposecan easily be conceived by those skilled in the present art. If thealternative embodiment is adopted, the information retrieving equalizercan be designed to accommodate for correlated noise, either directly, orby adopting a noise whitening filter preceding it.

In yet another embodiment, the ECC is chosen to be a turbo code withparallel concatenation, or, alternatively a low-density parity checkcode, whereas the decoding is declared terminated after a sufficientnumber of decoding iterations, including a possible additional outercode protecting against a possible error floor formation.

In an alternative embodiment the information retrieval can be performedwith information retrieving equalizer as an integral part of theiterative decoder, with the reliabilities of the information symbolsiteratively exchanged between the decoder and the information retrievingequalizer. In this case, an optional recursive pre-coder can be includedinto the communication system, prior to the waveform shaping at thetransmitter.

In another instance the information retrieving equalizer can beimplemented as a soft output Viterbi detector, or any simplification ofthe aforementioned algorithms/approaches, including the application ofthe “per survivor” processing.

Referring to the figures, FIG. 1 shows a general schematic of a digitalcommunication system. In general a communication system comprises of atransmitter, channel and receiver blocks. Within the transmitter, thefollowing parts are discernible: Input information stream (110), anerror control encoder (120), followed by an optional channel pre-coder(130), as well as the pulse-shaping block (140), responsible for shapingof the transmitted information-bearing waveforms. The receiver, on theother hand, comprises: a receiving filter (150), a sampler (160), ananalog-to-digital converter (170), a channel impairments' mitigatingequalizer (180), a channel response reshaping block at which the presentinvention is primarily aimed at (190), an information-retrievingequalizer (200), a decoder (210), concluding with an output informationstream (220).

FIG. 2 shows an exemplary flow diagram of the channel adjustment block.The operation of the channel adjustment block comprises of two phases:(i) training phase and (ii) data detection phase. In the training phasethe channel response is acquired by one of the well-known strategies,e.g. by means of training sequences, or pilot tones, or by blindacquisition. The channel response is, then compared to a target responseset by the system designer, and if necessary, channel adjustmentcoefficients are determined next. The determined adjustment coefficientsare then used in the second, data detection phase, resulting in aneffective shortening of the original channel response. In time-varyingchannels, the training phase is repeated as often as the channelcondition (response) is changed sufficiently so as to warrant additionaladjustment to the target response.

FIG. 3 shows an example of the channel response adjustment.Specifically, part (a) shows a direct channel response to a single inputsymbol that is 8 symbol slots long. Part (b) shows an outcome of achannel response reshaping. As can be seen, after channel responseadjustment, the response length is reduced to only 4 important samples(instead of the original 8), allowing a 16-fold simpler informationretrieving equalizer utilization (for a binary input alphabet).

FIG. 4 illustrates an improved performance of the bandwidth constrainedsystem in the embodiment described in this invention (in solid lines),compared to performance of standard QAM systems (dashed lines), for sameinstances of spectral efficiencies.

Accordingly, one aspect of the invention is an apparatus comprising atransmitter which contains a plurality of elements including:

(a) an error control code encoder used to append redundant informationso as to avail information symbols' retrieval in the presence of noiseand impairments, wherein the code is designed for attainment ofperformance closer to the constrained bandwidth channel capacity; and

(b) a receiver comprising a plurality of elements conducive to theretrieval of the transmitted information symbols, including aninformation retrieving equalizer and an error control decoder for thecode employed in the transmitter; wherein the apparatus is for use in adigital communication system conveying information symbols at a certainsymbol rate in which the information bearing waveforms are filtered to abandwidth significantly narrower than the communication symbol rate; and

wherein the apparatus achieves an improved performance and/or anincreased efficiency in information transmission in abandwidth-constrained communication system as compared with systems notemploying the bandwidth constraint.

In one alternative the transmitter contains a plurality of error controlencoders and the receiver contains a plurality of decoders,corresponding to the encoders in the transmitter, availing the retrievalof information symbols. In another alternative the apparatus furthercomprises one or more code interleavers at the transmitter used tosuccessively, in parallel, or both successively and in parallel encodethe information symbols prior to transmission designed so as to reachthe capacity of the channel with memory and further comprising one, ormore code de-interleavers in the receiver, undoing the interleavingaction performed at the transmitter, on the course of the process ofinformation symbols detection. In yet another alternative the apparatusfurther comprises a receiving filter. In still another alternative thereceiver further comprises a transmission impairments mitigatingequalizer. In still another alternative the receiver further comprises achannel response shortening equalizer to attain improved performance. Instill another alternative the information retrieving equalizer outputsthe reliability estimates, often referred to as the soft information, asto the information symbols. In still other alternatives, the informationretrieving equalizer functions as a maximum a posteriori equalizer, as atrellis-based equalizer, as a sliding window variation of a maximum aposteriori equalizer, or as a sliding window variation of a soft outputequalizer or takes advantage of per survivor processing.

Another aspect of the invention is a communication system incorporatingthe apparatus as described above that employs iterative detection,wherein the information retrieving equalizer can output likelihoodestimates (often referred to as soft information) on the receivedsymbols and pass it on to the error control decoders with those (i.e.the equalizer and the decoder(s)) iteratively exchanging their estimateson the received information for a number of times.

Yet another aspect of the invention is a communication systemincorporating the apparatus as described above wherein the receiveremploys error control code symbol detection by a numerical optimizationprocedure.

Yet another aspect of the invention is a communication systemincorporating the apparatus as described above wherein the receiveremploys joint channel and error control code symbol detection by anumerical optimization procedure.

Yet another aspect of the invention is a communication systemincorporating the apparatus as described above wherein in the receiveremploys joint channel and error control code symbol detection by acombination of iterative decoding and a numerical optimizationprocedure.

While the present invention has been described above in terms ofspecific embodiments, it is to be understood that the invention is notlimited to these disclosed embodiments. Upon reading the teachings ofthis disclosure many modifications and other embodiments of theinvention will come to mind of those skilled in the art to which thisinvention pertains, and which are intended to be and are covered by boththis disclosure and the appended claims. It is indeed intended that thescope of the invention should be determined by proper interpretation andconstruction of the appended claims and their legal equivalents, asunderstood by those of skill in the art relying upon the disclosure inthis specification and the attached drawings.

The following patents and patent application publications are cited.These patents and patent application publications are not necessarilyprior art: U.S. Pat. No. 8,155,530 (Alic); U.S. Pat. No. 7,012,974 B1(Liu); U.S. Pat. No. 4,888,775 A (Karabed); U.S. Pat. No. 7,257,172 B2(Okamoto); EP 0677965 A2 (Kim); WO 2013101583 A1 (Yu); US 20130332790 A1(Lu); US 20120213267 A1 (Stojanovic); U.S. Pat. No. 7,205,912 B1 (Yang);US 20030161062 A1 (Akamatsu); U.S. Pat. No. 7,852,965 (Feller); WO2005015750 A1 (Kluger); U.S. Pat. No. 6,377,529 (Lee); U.S. Pat. No.5,430,744 (Fettweis); U.S. Pat. No. 7,839,924 (Yamaguchi); U.S. Pat. No.6,385,255 (Fan); U.S. Pat. No. 5,757,855 (Jaffe); US20130332790 A1 (Lu);WO2010066778 A1 (Theis); U.S. Pat. No. 7,180,955 (Gatherer); U.S. Pat.No. 6,269,129 B1(Rhee); and U.S. Pat. No. 8,595,590 B1 (Vojcic).

The following non-patent publications are cited. These non-patentpublications are not necessary prior art: Tom V. Souvignier, Mats Öberg,Paul H. Siegel, Robert E. Swanson, Jack K. Wolf, “Turbo Decoding forPartial Response Channels” IEEE TRANSACTIONS ON COM-MUNICATIONS, VOL.48, NO. 8, (2000); S. Benedetto, D. Divsalar, G. Montorsi, F. Pollara,“A Soft-Input Soft-Output APP Module for Iterative Decoding ofConcatenated Codes”, IEEE COMMUN. LETT., VOL. 1, NO. 1, (1997); and L.Bahl, J. Cocke, F. Jelinek, and J. Raviv, “Optimal Decoding of LinearCodes for minimizing symbol error rate”, IEEE Transactions onInformation Theory, vol. IT-20(2), pp. 284-287, (1974).

ADVANTAGES OF THE INVENTION

The present invention provides a receiver design and system suitable foruse in an environment involving bandwidth constraint with lowercomplexity, latency, and power dissipation. By an appropriatecombination of equalization and error control coding, the overall systemperformance and capacity are improved. The invention is based on acompletely new insight, based on a novel theoretical finding thatimplies a superior performance than suspected ever before. The previousconstructs do not come close to the predictions of the new theory.

The present invention possesses industrial applicability as a receiverdesign with improved performance in a bandwidth-constrained environmentand as a method for use of the receiver design.

The method claims of the present invention provide specific method stepsthat are more than general applications of laws of nature and requirethat those practicing the method steps employ steps other than thoseconventionally known in the art, in addition to the specificapplications of laws of nature recited or implied in the claims, andthus confine the scope of the claims to the specific applicationsrecited therein. The method steps require the use of specific hardwareand involve specific processes involving the hardware that generate achange in physical state of the hardware.

The inventions illustratively described herein can suitably be practicedin the absence of any element or elements, limitation or limitations,not specifically disclosed herein. Thus, for example, the terms“comprising,” “including,” “containing,” etc. shall be read expansivelyand without limitation. Additionally, the terms and expressions employedherein have been used as terms of description and not of limitation, andthere is no intention in the use of such terms and expressions ofexcluding any equivalents of the future shown and described or anyportion thereof, and it is recognized that various modifications arepossible within the scope of the invention claimed. Thus, it should beunderstood that although the present invention has been specificallydisclosed by preferred embodiments and optional features, modificationand variation of the inventions herein disclosed can be resorted bythose skilled in the art, and that such modifications and variations areconsidered to be within the scope of the inventions disclosed herein.The inventions have been described broadly and generically herein. Eachof the narrower species and subgeneric groupings falling within thescope of the generic disclosure also form part of these inventions. Thisincludes the generic description of each invention with a proviso ornegative limitation removing any subject matter from the genus,regardless of whether or not the excised materials specifically residedtherein.

It is also to be understood that the above description is intended to beillustrative and not restrictive. Many embodiments will be apparent tothose of in the art upon reviewing the above description. The scope ofthe invention should therefore, be determined not with reference to theabove description, but should instead be determined with reference tothe appended claims, along with the full scope of equivalents to whichsuch claims are entitled. The disclosures of all articles andreferences, including patent publications, are incorporated herein byreference.

What is claimed is:
 1. An apparatus comprising a transmitter whichcontains a plurality of elements including: (a) an error control codeencoder used to append redundant information so as to avail informationsymbols' retrieval in the presence of noise and impairments, wherein thecode is designed for attainment of performance closer to the constrainedbandwidth channel capacity; and (b) a receiver comprising a plurality ofelements conducive to the retrieval of the transmitted informationsymbols, including an information retrieving equalizer and an errorcontrol decoder for the code employed in the transmitter; wherein theapparatus is for use in a digital communication system conveyinginformation symbols at a certain symbol rate in which the informationbearing waveforms are filtered to a bandwidth significantly narrowerthan the communication symbol rate; and wherein the apparatus achievesan improved performance and/or an increased efficiency in informationtransmission in a bandwidth-constrained communication system as comparedwith systems not employing the bandwidth constraint.
 2. The apparatus ofclaim 1 wherein the transmitter contains a plurality of error controlencoders and the receiver contains a plurality of decoders,corresponding to the encoders in the transmitter, availing the retrievalof information symbols.
 3. The apparatus of claim 1 further comprisingone or more code interleavers at the transmitter used to successively,in parallel, or both successively and in parallel encode the informationsymbols prior to transmission designed so as to reach the capacity ofthe channel with memory and further comprising one, or more codede-interleavers in the receiver, undoing the interleaving actionperformed at the transmitter, on the course of the process ofinformation symbols detection.
 4. The apparatus of claim 1 wherein theapparatus further comprises a receiving filter.
 5. The apparatus ofclaim 1 wherein the receiver further comprises a transmissionimpairments mitigating equalizer.
 6. The apparatus of claim 1 whereinthe receiver further comprises a channel response shortening equalizerto attain improved performance.
 7. The apparatus of claim 1 wherein theinformation retrieving equalizer outputs the reliability estimates,often referred to as the soft information, as to the informationsymbols.
 8. The apparatus of claim 1 wherein the information retrievingequalizer functions as a maximum a posteriori equalizer.
 9. Theapparatus of claim 1 wherein the information receiving equalizerfunctions as a trellis-based equalizer.
 10. The apparatus of claim 1wherein the information receiving equalizer takes advantage of persurvivor processing.
 11. The apparatus of claim 1 wherein theinformation receiving equalizer functions as a sliding window variationof a maximum a posteriori equalizer.
 12. The apparatus of claim 1wherein the information receiving equalizer functions as a slidingwindow variation of a soft output equalizer.
 13. A communication systemincorporating the apparatus of claim 1 that employs iterative detection,wherein the information retrieving equalizer can output likelihoodestimates (often referred to as soft information) on the receivedsymbols and pass it on to the error control decoders with those (i.e.the equalizer and the decoder(s)) iteratively exchanging their estimateson the received information for a number of times.
 14. A communicationsystem incorporating the apparatus of claim 1 wherein the receiveremploys error control code symbol detection by a numerical optimizationprocedure.
 15. A communication system incorporating the apparatus ofclaim 1 wherein the receiver employs joint channel and error controlcode symbol detection by a numerical optimization procedure.
 16. Acommunication system recited in claim 1 wherein in the receiver employsjoint channel and error control code symbol detection by a combinationof iterative decoding and a numerical optimization procedure.